Guidance and control of an ASV in AUV tracking operations

Guidance and control of an ASV in AUV tracking operations José Melo, Aníbal Matos Faculdade de Engenharia da Universidade do Porto R. Dr. Roberto Fria...
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Guidance and control of an ASV in AUV tracking operations José Melo, Aníbal Matos Faculdade de Engenharia da Universidade do Porto R. Dr. Roberto Frias 4200-465 Porto Portugal {jose.melo, anibal}@fe.up.pt

Abstract— The following addresses the control of an Autonomous Surface Vehicle (ASV) to follow the trajectory made by an Autonomous Underwater Vehicle (AUV) when the last is performing any given pre-programmed mission. In fact, it has been proved to be of great interest to have an ASV that could follow on the surface and even catch up the trajectory performed by the AUV, when executing a given mission. In order to achieve this desired coordinated motion between AUV and ASV, it would make sense just to program each of the vehicles with the same mission. However, due to the nature of vehicles, missions and also due to the localization system used, with this kind of solution some problems would arise, namely related with timings and synchronization, which are indeed difficult to overcome. The solution proposed here tries to estimate the AUV position, by tapping the signals exchanged between the former and each of the beacons of the acoustic localization network, and control and actuate the ASV in accordance.

II. E XPERIMENTAL S ETUP The vehicles used within this work are the ASV Zarco and the AUV MARES, both developed by the OSG. With the vehicles it is also used and acoustic Long Baseline network, with a set of two acoustic beacons or buoys. To decrease the complexity of the setup, only 2 buoys are used as this configuration enables the correct estimate of the AUV while minimizing the number of buoys in use. Each of the buoys is equipped with the appropriate transceiver which allows them to listen to acoustic signals and emit an appropriate answering signal when needed.

I. I NTRODUCTION The Ocean Systems Group (OSG), a study group within the Institute of Systems and Robotics, Porto (ISR), an institute/laboratory associated with the Faculty of Engineering, University of Porto (FEUP), has its main research efforts directed toward the development of advanced systems for the automatic collection and processing of data in aquatic environments. Specifically, the OSG developed a set of robotic autonomous aquatic vehicles which are used in very different kind of missions. Nowadays there is an increasing demand for real-time data which can support some of the research being done by the OSG. However, reliable communications with underwater vehicles, namely with Autonomous Underwater Vehicles (AUVs) are quite difficult to establish due to the physical properties of the water, specially when transmitting along large distances. Having a Autonomous Surface Vehicle (ASV) acting as a support boat by following the AUV trajectory, while this last one performs any given mission, would provide a way for the establishment of a communication link between both vehicles and therefore the ability to communicate in real time with the AUV. This would be in fact a big enhancement, providing the technical background for more complex and challenging missions.

978-1-4244-2620-1/08/$25.00 ©2008 IEEE

Fig. 1.

Acoustic Beacon

The AUV MARES [1] is a highly modular small sized AUV, with about 1.5m long and weighting about 32kgs, and propelled by 4 motors which drive the vehicle to velocities up to 3m/s. The disposition of the motors provides the vehicle with a high manuveurability meaning that the vehicle horizontal motion is almost decoupled from the vertical one. Prior to any mission, the vehicle is informed about the actual global coordinates of the two beacons that constitute the acoustic network used. Then, in order to know its exact localization at

any given time, it has to interrogate each beacon, sending an acoustic signal with a specific frequency and waiting for the beacon reply. By timing this acoustic events, it is then possible to compute the actual distance of a given vehicle to each of the two beacons and, therefore, its real-time global coordinates. To navigate in between two consecutive queues, the AUV uses the information provided by set of dead-reckoning instruments.

way do detect spurious measurements. The last stage of the estimation of the AUV position is a recursive least squares algorithm with forgetting factor which accurately predicts the motion of the vehicle based on a straight-line model.

Fig. 4.

Bloc Diagram of the Estimation algorithm

A. Range Estimation

Fig. 2.

AUV MARES

The algorithm to estimate distances d1 and d2 , as can be seen on figure 5, is based on a algorithm proposed in [3] and assumes that the AUV positions remains stationary between the interrogation of the beacon and the reception of the correspondent answer. It is also considered that the depths the AUV reaches while in mission are constant and quite small relative to the distances to both beacons and, thereby, we can assume only motion in the horizontal plane.

The Autonomous Surface Vehicle also used, the ASV Zarco [2], is a small sized catamaran based craft, designed to operate in quiet water, and can reach speeds of up to 2m/s. This vehicle can be not only automatically operated, performing any given pre-programed mission, but also remotely operated if connected to the shore base by the WiFi link it possesses. This vehicle possesses a set of navigation instruments, including a high-precision GPS receiver, which provide an accurate positioning level. The vehicle can also operate as an acoustic beacon, being part of an acoustic network, as it is also equipped with the necessary transceiver. Fig. 5. Configuration of a typical mission, with the buoys and the AUV depicted

The AUV interrogates both beacons in a cyclic way, as shown on figure 6. By timing all the detections of each buoy, it is then possible to compute the distance to the AUV, d1 and d2 ,with a prior knowledge the delays associated with this communications and considering a constant sound propagation speed on the water. B. Kalman Filter

Fig. 3.

ASV Zarco

III. E STIMATION The estimation algorithm is a three stage algorithm. On the first stage the distances between AUV and each of the acoustic beacons are estimated. The second stage is an Extended Kalman Filter, which provides a nice position estimation and also a low-pass filter process which provides an efficient

This first stage it is then responsible for estimating the range measurements, from the AUV to each of the beacons in use. However, what is needed is the AUV positions and velocities in reference to an earth-fixed reference or, in other words, the AUV state. By using a continuous-discrete Kalman Filter and given the position of each buoy in reference to the frame in use, it is possible then to get an estimate to the AUV state. The model used to predict the AUV motion is given by (1). It can be seen that this model is a very simple one, only accounting for the factor β, an exponential decay of the velocity, assuring that in case of malfunctioning of the system, the vehicle will eventually stop.

Fig. 6.

of information to obtain the velocities (vx , vy ). The main idea is to use the data output by the Kalman Filter (t, x, y), and to estimate the parameters of a straight line that best fits the points (x, y) along the time t. By doing so we are optimizing these estimates for straight line motion, meaning this then whenever the AUV changes direction, poorer results are expected. Considering that a straight line in the XY frame can be described by the equations (5), the parameters x0 , y0 , vx , and vy are estimated with a LSE where the forgetting factor λ weights the past terms in the estimate as desired [5]. This weighting factor will be of most importance specially on the change of direction, and a trade-off between a good straightline and turning motion must be achieved.

Timeline describing an interrogation cycle for the AUV







0 1 x˙  v˙x   0 β     y˙  =  0 0 0 0 v˙y



x(t) = x0 + vx t y(t) = y0 + vy t



x 0 0  vx  0 0    0 1  y  vy 0 β

IV. C ONTROL AND ACTUATION (1)

The Kalman Filter uses the set of discrete equations (2) to correct the estimate of the AUV state whenever there are new range measurements, while equations (3) are a continuous approximation of the evolution of the motion of the vehicle and are used to update the state estimates between two consecutive range measurements. Sk Kk Xk Pk Xn Pn

= = = =

HPk− H T + rs Pk− H T Sk−1 Xk− + Kk (zk − zk∗ ) (I − Kk H)Pk−

= eAt X + Rt T T = eAt (P + + 0 e−As Qe−A s ds)eA t

(2)

k

The second part of the work consists on actuating the ASV properly so that the trajectory performed by both vehicles is similar. For that, a strategy that enables the ASV to reach and follow up the AUV trajectory had to be chosen. In order to do that the relative distance from the AUV to the ASV, but also the heading of the ASV relative to the trajectory the AUV is undergoing, needs to be known. From [3] and [6] it was possible to derive a simplified model for the forces and moments interacting with the ASV. In (6) it can be seen that the simplified model only accounts for longitudinal and lateral forces, and lateral moment, X, Y and N , respectively. X Y N

(3)

The model is indeed very simple and even though the estimates of the position are quite accurate, the estimates for the velocities are not as precise as desired. However, the Kalman Filter has a very important role in the estimation process, as it allows the elimination of spurious data measurements, by evaluating the covariance of the error associated with the measurements as in (4), and comparing it to the design parameter γ [4]. kzk − zk∗ kS −1 ≤ γ

(5)

(4)

C. Least Squares The Kalman Filter produces nice estimates of the AUV position (x, y), but fails when it comes to produce accurate estimates of the vehicle velocity (vx , vy ), mostly because the model used does not include sufficient information about the vehicle motion. To overcome this, a Least Squares Estimator (LSE) with Forgetting is used. As most of the AUV motion on every mission can be described as straight line, we use this piece

= m(u˙ − vr) = m(v˙ − ur) = Iz r˙

(6)

Having equations (6) as a starting point it is possible to design a simplified decoupled control of the vehicle, with minimal performance drawbacks and huge advantages on implementation. Therefore, the ASV can be controlled almost independently in heading and position. Both controllers will be further discussed in detail on sections ahead. A. Control Law Based on the track-keeping systems referred in [6], it was possible to derive a simplified kinematics equation to the ASV that synthesizes the desired behaviour. We can see it in (7), where u is the forward speed (surge) and Cy represents any water current that may exist. It is assumed that u > |Cy |, meaning this that the actuation is powerful enough to overcome the disturbances. y˙ = u sin(ψ) + Cy

(7)

For a matter of simplicity, it can be assumed that the AUV follows a trajectory coincident with the X, as generalized trajectories can be easily derived from such an assumption.

The main idea of the strategy adopted is that if the ASV is far enough from the AUV, then it should go straight ahead on a direction perpendicular to the ASV direction on full speed; as it approaches the AUV, it should start changing its heading to one that suits it needs. On figure 7 is depicted the desired behaviour.

Fig. 7.

ψ is our control variable and goes directly to the heading loop control. As we are in presence of disturbances, like the water currents, which are often difficult to know, it is also necessary to take in account an additional state that ensures a null steady state tracking error. k1 and k2 are design constants and account for the distance y from where the ASV should start adjusting it’s speed and heading. The control variable φ is obtained by: ψ = − arcsin(k1 y + k2 l)

(8)

where    0 ˙l = 0   y

if if

l> l
0 ∨ y

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